Normed Rings and Spectral Representation

  • Kôsaku Yosida
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 123)


A linear space A over a scalar field (F) is said to be an algebra or a ring over (F), if to each pair of elements x, yA a unique product xyA is defined with the properties:
$$\left. {\begin{array}{*{20}{c}}{\left( {xy} \right)\,z\, = \,x\left( {yz} \right)\,\,\,\left( {associativity} \right),} \\ {x\left( {y\, + \,z} \right)\, = \,xy\, + \,xz\,\,\,\left( {distributivity} \right)} \\ {\alpha \beta \,\left( {xy} \right)\, = \,\left( {\alpha x} \right)\,\left( {\beta y} \right).} \end{array},\,\,\,\,\,\,\,\,\,\,\,} \right\}$$


Hilbert Space Spectral Representation Maximal Ideal Symmetric Operator Normed Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • Kôsaku Yosida
    • 1
  1. 1.Kamakura, 247Japan

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